As an exercise, I've tried the same a while ago and stumbled upon the same problem. I've solved it by calculating the bounding box first, as you have described it and then I wrote my own warping function. Warping is very simple, however you need to do lerp by yourself.
As some pixel-wise weighting is required anyways for good results (like multiple pixels from different images might end up on the same output pixel and thus need to be blended), I did not feel bad of abandoning cvWarpPerspective.
I think you're on the right track. You need to account for the image translation that happened when you moved the image.
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